In this article, we study the pointwise asymptotic behavior of iterated convolutions on the one-dimensional lattice Z. We generalize the so-called local limit theorem in probability theory to complex-valued sequences. A sharp rate of convergence toward an explicitly computable attractor is proved together with a generalized Gaussian bound for the asymptotic expansion up to any order of the iterated convolution.
Local Limit Theorem for Complex-Valued Sequences
Coeuret, Lucas
2025
Abstract
In this article, we study the pointwise asymptotic behavior of iterated convolutions on the one-dimensional lattice Z. We generalize the so-called local limit theorem in probability theory to complex-valued sequences. A sharp rate of convergence toward an explicitly computable attractor is proved together with a generalized Gaussian bound for the asymptotic expansion up to any order of the iterated convolution.
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